LONG-TERM MONITORING STRATEGY FOR CONCRETE-BASED STRUCTURES USING NONLINEAR KALMAN FILTERING K.A. Snyder 1 , Z.Q. Lu 1 , and J. Philip 2 1 National Institute of Standards and Technology, Gaithersburg, MD USA 2 U.S. Nuclear Regulatory Commission, Rockville, MD USA ABSTRACT Kalman filtering is introduced as a rational means for developing a monitoring strategy for concrete structures. The mathematics and utility of linear Kalman filters are presented briefly, and the use of linear filters is demon- strated for Fickian diffusion. The nonlinear extended Kalman filter is introduced and its utility in estimating a transport parameter is demonstrated. The concrete service life computer program 4SIGHT is introduced briefly and combined with nonlinear filtering to refine the transport coefficient from a laboratory diffusion experiment. A fictitious monitoring strategy is presented that uses Kalman filtering to both refine estimates and extend the time between monitoring intervals. The advantages of using Kalman filtering, along with the remaining technical difficulties, are discussed. Keywords: concrete; Kalman filter; monitoring; performance assessment; service life. 1 - INTRODUCTION Virtually all failures of concrete structures can be attributed to chemical attack, either from without (sulfate attack, corrosion of the steel reinforcement, etc.) or from within the structure (alkali silica, etc.). The specific degradation mechanism causing the failure may be either unforeseen or the rate of advancement may be underestimated. Most concrete structures in the United States are still designed and built using historical knowledge that has been tabulated in engineering manuals of practice, which do not address a specific structure and its environment. Computer models exist for predicting concrete performance based on the cement properties, the concrete mixture design, and the structure’s environment. Unfortunately, these models are used in only a small fraction of new construction. The best of these computer models have achieved an adolescent stage of development; they are technically sophis- ticated but still have not incorporated all the complexity of concrete. Given this stage of technical advancement in concrete service life models, it is unreasonable to expect any model to accurately predict performance with a high degree of certainty, especially over very long time scales (e.g., centuries or millennia). By analogy, a Professional Engineer (PE) will sign the drawings of a structural design, thereby staking his or her professional reputation on the structural performance. It would be rare, however, for a concrete materials engineer to stake their reputation by signing a corresponding statement of durability that a concrete structure will achieve the design service life. This state of technical achievement is an important point for the construction of critical infrastructure concrete components. If there are no computer models that are absolutely reliable, the only sensible alternative is to develop a supplemental monitoring strategy. Ideally, this strategy would combine both computer model predictions and periodic measurements. Kalman filtering [1] is one way to mathematically combine such data. Moreover, the technique is optimized so that after combining both the model prediction and the physical measurement, the uncertainty is less than that for either one individually. This idea is not new. Kalman filtering has already been incorporated into hydrogeological modeling [2, 3] and the study of porous building materials [4]. The Kalman filter is introduced and applied to various artificial scenarios. The linear filter is applied to a Fickian diffusion problem. The nonlinear filter is introduced as a means of parameter estimation in Fickian problems. The 4SIGHT computer model is introduced to highlight constraints that may arise in using Kalman filters with computer service life models for concrete. A fictitious monitoring scenario is presented to demonstrate how Kalman filtering may extend the time between measurements and simultaneously reduce uncertainty. 2 - LINEAR KALMAN FILTER Let there be a vector x that is a list {x 0 , x 1 ,..., x n } of all the quantities (internal field variables, transport parameters, etc.) that a performance assessment model needs to predict the future time-dependent behavior of a system. In addition, there may also be external control variables u. For a linear model, the vector advances from time t k-1 to time t k , by a linear transformation from x k-1 to x k effected by a matrix propagator A. If the transformation is a